PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
975110^90661+237390662Patrick De Geest11/2018
975210^90661-19478190661Patrick De Geest07/2019
97533*5^129698+890656Lelio R Paula10/2014
9754F(433781)90655Henri Lifchitz09/2003
975519^70891+8290653Lelio R Paula06/2016
9756(29*2^301124-1)/1390648Lelio R Paula02/2014
975710^90636+6415990637Patrick De Geest07/2019
975810^90636-310190636Patrick De Geest11/2018
97597*3^189953-890632Lelio R Paula08/2014
976010^90626+33928990627Patrick De Geest07/2019
976110^90626-113190626Patrick De Geest11/2018
976211^87022-180090625Enzo Doria12/2012
976310^90623+86190624Patrick De Geest11/2018
976410^90623-30584190623Patrick De Geest07/2019
9765(2^301042+47)/1203696990616Lelio R Paula06/2013
97662^301004-278693990612Enzo Doria03/2016
976710^90611+16997790612Patrick De Geest07/2019
976910^90611-973790611Patrick De Geest11/2018
976810^90610+3674790611Patrick De Geest07/2019
977010^90609+682390610Patrick De Geest11/2018
977110^90610-2657390610Patrick De Geest07/2019
977210^90609-22817390609Patrick De Geest07/2019
97732^300980-2790605Lelio R Paula11/2012
97742*10^90597-790598Dmitry Domanov11/2010
9775197^39485+290597Lelio R Paula06/2013
97767^107198+4890593Lelio R Paula04/2016
9777(86*10^90588+121)/990589Robert Price03/2017
97782^300923+5390587Lelio R Paula11/2012
97792^300874+790573Lelio R Paula10/2012
978010^90567+948990568Patrick De Geest11/2018
978110^90567-23135390567Patrick De Geest07/2019
9782(2^300857+2214)/290567Stefano Morozzi01/2020
97835^129568-5690565Lelio R Paula04/2016
97842^300847-11283190564Enzo Doria06/2014
978510^90562+79019790563Patrick De Geest07/2019
978610^90562-298190562Patrick De Geest11/2018
9787(7796^23269-1)/779590557Serge Batalov08/2020
9788(31*10^90554+257)/990555Robert Price12/2021
978910^90549+381190550Patrick De Geest11/2018
979010^90549-63030390549Patrick De Geest07/2019
97912^300790-454190547Yves Minet03/2019
979210^90532+816990533Patrick De Geest11/2018
979310^90531+983190532Patrick De Geest11/2018
979410^90532-15488990532Patrick De Geest07/2019
979510^90531-106058990531Patrick De Geest07/2019
97972^300718+25525590526Lelio R Paula02/2016
9796(2^300719+938)/290526Stefano Morozzi01/2020
979810^90516+21591790517Patrick De Geest07/2019
979910^90516-678390516Patrick De Geest11/2018
980010^90511+3017790512Patrick De Geest07/2019
980110^90511-697790511Patrick De Geest11/2018
9802(8573^23011-1)/857290502Serge Batalov08/2020
98032^300637+9590501Lelio R Paula11/2012
98047^107087-2490500Lelio R Paula04/2016
980510^90499+19154790500Patrick De Geest07/2019
980610^90499-582390499Patrick De Geest11/2018
9808(10^90499+3^90499)/1390498Robert Price01/2013
980713^81241+9090498Lelio R Paula06/2016
9809(2^300600+1222)/290490Stefano Morozzi01/2020
981010^90480+513190481Patrick De Geest11/2018
981110^90480-8572190480Patrick De Geest07/2019
9812(34*10^90478-547)/990479Robert Price03/2021
98136^116273-8590478Lelio R Paula05/2016
981410^90473+313990474Patrick De Geest11/2018
981510^90473-15059990473Patrick De Geest07/2019
981610^90470+231990471Patrick De Geest11/2018
981710^90470-7163790470Patrick De Geest07/2019
98186^116256-1757390465Enzo Doria02/2013
98192^300502+5461590461Lelio R Paula02/2016
9820(13*2^300487+1)/4590456Lelio R Paula09/2013
982110^90453+14184390454Patrick De Geest07/2019
982310^90453-396990453Patrick De Geest11/2018
982210^90452+5931790453Patrick De Geest05/2021
982410^90452-8000000190452Robert Price04/2021
982510^90452-8471390452Patrick De Geest05/2021
982610^90440+135990441Patrick De Geest11/2018
982710^90440-1882190440Patrick De Geest07/2019
9828(3^189545-8)/590436Lelio R Paula01/2013
9829(7*2^300406-1)/390432Lelio R Paula02/2014
983010^90430+333990431Patrick De Geest11/2018
983110^90430-6347790430Patrick De Geest07/2019
9832(5408^24223-1)/540790422Serge Batalov08/2020
983310^90414+22959390415Patrick De Geest07/2019
983410^90414-154790414Patrick De Geest11/2018
983510^90404+4704190405Patrick De Geest07/2019
983610^90404-642990404Patrick De Geest11/2018
983710^90401+207790402Patrick De Geest11/2018
983810^90401-36863790401Patrick De Geest07/2019
983924900^4271+4271^2490090401Hans Havermann08/2020
98404*5^129332+390400Lelio R Paula10/2014
984210^90397+1978390398Patrick De Geest07/2019
984123380^7353+7353^2338090398Hans Havermann08/2020
984410^90397-32390397Patrick De Geest11/2018
9843(2^300293+2762)/290397Stefano Morozzi01/2020
984524058^5719+5719^2405890394Hans Havermann08/2020
98462^300249-1624590384Enzo Doria04/2013
984724414^5035+5035^2441490381Hans Havermann08/2020
9848(7*10^90371-313)/990371Robert Price11/2016
984910^90363+5867790364Patrick De Geest07/2019
985010^90363-355790363Patrick De Geest11/2018
985110^90358+10464190359Patrick De Geest07/2019
98542*6^116118+790358Lelio R Paula10/2014
985310^90358-497990358Patrick De Geest11/2018
985210^90357+11283790358Patrick De Geest07/2019
985510^90357-18959390357Patrick De Geest07/2019
985610^90356+5311390357Patrick De Geest07/2019
985710^90356-719790356Patrick De Geest11/2018
985810^90353+60321190354Patrick De Geest07/2019
985910^90353-108990353Patrick De Geest11/2018
9860(24737*2^300101+1)/2590343Lelio R Paula06/2014
98614*10^90334-2190335Robert Price04/2016
9862(4546^24697-1)/454590329Serge Batalov08/2020
986310^90322+13769190323Patrick De Geest07/2019
986410^90322-955190322Patrick De Geest11/2018
986510^90316+999190317Patrick De Geest11/2018
9866(4550^24691-1)/454990317Serge Batalov08/2020
986710^90316-4562790316Patrick De Geest07/2019
986810^90315+3288990316Patrick De Geest07/2019
98702^300019-11033590315Enzo Doria05/2014
986910^90315-856190315Patrick De Geest11/2018
9871FAB2(300001,5032)90310Robert Price05/2019
9872FAB2(300001,29405)90310Robert Price05/2019
9873(2^299965+2774)/290299Stefano Morozzi01/2020
987423679^6506+6506^2367990296Hans Havermann08/2020
98752^299949-100590294Lelio R Paula11/2013
9876(2^299947+2054)/290293Stefano Morozzi01/2020
987721740^14229+14229^2174090291Hans Havermann08/2020
987810^90279+6245790280Patrick De Geest07/2019
987910^90279-155190279Patrick De Geest09/2018
9880(2^299892+1986)/290277Stefano Morozzi01/2020
9881(2^299893+3866)/290277Stefano Morozzi01/2020
98822^299868-10961390270Enzo Doria04/2014
988310^90259+35929990260Patrick De Geest07/2019
988410^90259-944390259Patrick De Geest09/2018
9885(2^299831+3786)/290258Stefano Morozzi01/2020
988610^90252+10287390253Patrick De Geest07/2019
988710^90252-810390252Patrick De Geest09/2018
98885*2^299799-390250Lelio R Paula08/2014
9889(2^299803+3326)/290250Stefano Morozzi01/2020
989013^81008-290239Lelio R Paula09/2013
989180697!4-25690234Robert Price11/2019
989364^49957-63^4995790232Robert Price07/2013
9892(2^299745+2994)/290232Stefano Morozzi01/2020
989410^90227+5628190228Patrick De Geest06/2016
98982^299725+31590227Lelio R Paula11/2013
989510^90227-100000000190227Robert Price05/2016
989610^90227-6876390227Patrick De Geest06/2016
98979*10^90226+2990227Robert Price03/2022
98995^129082+4890225Lelio R Paula03/2016
99002^299699+19590219Lelio R Paula10/2012
9901(55*10^90211-1)/990212Ray Chandler02/2012
990222131^11918+11918^2213190211Hans Havermann08/2020
990310^90209+897190210Patrick De Geest09/2018
990410^90209-72479790209Patrick De Geest07/2019
990510^90208+18953190209Patrick De Geest07/2019
990610^90208-224790208Patrick De Geest09/2018
9907(629^32233-1)/62890207Michael Stocker05/2020
9908116^43693-11590203Norbert Schneider08/2018
990910^90202+355390203Patrick De Geest09/2018
99103^189053+28090202Lelio R Paula04/2016
991110^90202-6779390202Patrick De Geest07/2019
99122^299639-18790201Lelio R Paula10/2012
991310^90199+25403190200Patrick De Geest07/2019
991410^90199-289190199Patrick De Geest09/2018
99162^299631+18390198Lelio R Paula10/2012
991521567^15212+15212^2156790198Hans Havermann08/2020
991710^90196+18753990197Patrick De Geest07/2019
991910^90196-968390196Patrick De Geest09/2018
991821708^14287+14287^2170890196Hans Havermann08/2020
992010^90193+10497390194Patrick De Geest07/2019
992110^90193-980990193Patrick De Geest09/2018
9922(21*2^299611-1)/2990192Lelio R Paula02/2014
9923(2277^26863-1)/227690186Serge Batalov08/2020
99242^299567+11390179Lelio R Paula10/2012
99252^299550+18990174Lelio R Paula10/2012
992610^90170+37606390171Patrick De Geest07/2019
992710^90170-674990170Patrick De Geest09/2018
9928(2^299535+3)/2990168Lelio R Paula01/2013
9929(2^299521+13)/1590164Stefano Morozzi03/2020
993022316^10971+10971^2231690163Hans Havermann08/2020
993110^90160+27194790161Patrick De Geest07/2019
993210^90160-561390160Patrick De Geest09/2018
9933(97*10^90155-1)/390157Serge Batalov12/2014
9934(29*10^90153+583)/990154Robert Price06/2021
99363^188938+868090147Lelio R Paula04/2016
993510^90146+16020990147Patrick De Geest07/2019
993710^90146-202790146Patrick De Geest09/2018
99386^115840-5590142Lelio R Paula05/2016
9939(5*10^90142-473)/990142Robert Price12/2017
99408*7^106659+590139Lelio R Paula10/2014
99412^299406-1665390131Enzo Doria05/2013
9942(317057^16384+1)/290131Richard Fischer10/2019
9943(2^299409+834)/290131Stefano Morozzi01/2020
994410^90128+28867390129Patrick De Geest07/2019
9946208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
994510^90128-838790128Patrick De Geest09/2018
9948(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
9947(5^128941-3^128941)/290126Kellen Shenton05/2022
99496^115819-5390125Lelio R Paula05/2016
995010^90123+631390124Patrick De Geest09/2018
99516^115816-1685390123Enzo Doria02/2013
995210^90123-2261790123Patrick De Geest07/2019
99536^115813-2390121Lelio R Paula05/2016
99542^299351-93307590114Paul Bourdelais04/2021
9955(22*10^90110+161)/390111Robert Price02/2017
9957(2^299330-509203)/6990106Lelio R Paula01/2013
995610^90105+91575990106Patrick De Geest07/2019
995810^90105-76790105Patrick De Geest09/2018
995910^90104+4818990105Patrick De Geest07/2019
9960(6050^23827-1)/604990105Serge Batalov08/2020
996210^90104-770390104Patrick De Geest09/2018
996310^90103+915990104Patrick De Geest09/2018
9961(797*10^90102-23)/990104Robert Price01/2022
996410^90103-20845790103Patrick De Geest07/2019
996510^90102+7301190103Patrick De Geest07/2019
996610^90102-60243390102Patrick De Geest07/2019
996710^90101+122553790102Patrick De Geest07/2019
996910^90101-320790101Patrick De Geest09/2018
996821730^14007+14007^2173090101Hans Havermann08/2020
9970(29*10^90096-17)/390097Erik Branger09/2014
9971(49*10^90094+221)/990095Robert Price02/2022
997210^90089+14318190090Patrick De Geest07/2019
997310^90089-357390089Patrick De Geest09/2018
99742^299247+187052990083Enzo Doria05/2016
997510^90079+160990080Patrick De Geest09/2018
997610^90079-23004390079Patrick De Geest07/2019
99772^299229-279778390077Enzo Doria04/2016
99782^299220-1631790075Enzo Doria04/2013
997911^86491-135090072Enzo Doria12/2012
998010^90071+5233390072Patrick De Geest07/2019
998210^90071-123390071Patrick De Geest09/2018
9981(314401^16384+1)/290071Richard Fischer10/2019
998310^90069+15852790070Patrick De Geest07/2019
998410^90069-784190069Patrick De Geest09/2018
9985(31*10^90064-1)/390066Robert Price03/2017
998610^90060+14943190061Patrick De Geest07/2019
998710^90060-83990060Patrick De Geest09/2018
998810^90052+236190053Patrick De Geest09/2018
998910^90052-9092990052Patrick De Geest07/2019
999010^90047+61990048Patrick De Geest09/2018
999110^90047-15107190047Patrick De Geest07/2019
9992L(430949)/861899/144038756153990045Serge Batalov07/2017
999322996^8233+8233^2299690043Hans Havermann08/2020
99942^299112+7395190042Enzo Doria04/2016
99958^99702+7^(99702-1)90040Robert Price02/2016
999610^90038+15780390039Patrick De Geest07/2019
999710^90038-968790038Patrick De Geest09/2018
99995*10^90033+390034Dmitry Domanov11/2010
9998(17574^21211-1)/1757390034Serge Batalov08/2020
1000010^90030+22581390031Patrick De Geest07/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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